#### Abstract

A framework is presented which allows an investigator to estimate the portion of the effect of one exposure that is attributable to an interaction with a second exposure. We show that when the two exposures are independent, the total effect of one exposure can be decomposed into a conditional effect of that exposure and a component due to interaction. The decomposition applies on difference or ratio scales. We discuss how the components can be estimated using standard regression models, and how these components can be used to evaluate the proportion of the total effect of the primary exposure attributable to the interaction with the second exposure. In the setting in which one of the exposures affects the other, so that the two are no longer independent, alternative decompositions are discussed. The various decompositions are illustrated with an example in genetic epidemiology.

#### Disciplines

Biostatistics | Epidemiology | Statistical Models

#### Suggested Citation

VanderWeele, Tyler J. and Tchetgen Tchetgen, Eric J., "Attributing effects to interactions" (July 2013). *Harvard University Biostatistics Working Paper Series.* Working Paper 162.

http://biostats.bepress.com/harvardbiostat/paper162